Trying to summarize Kant's influence on philosophy
is like trying to summarize Newton's influence on science. The most accurate
summation in either case may be: after Newton/Kant the entire approach
in all of science/philosophy had changed. We cannot capture those changes
in a clear summary, but we can identify some of the parts. Newton (along
with Leibniz) introduced
calculus without which the modern scientific revolution could not have
turned. Kant introduced a way of thinking about the relation of the human
mind to the objective world and established a powerful method of moral
reasoning. Kant changed the entire world by providing a new way of thinking
about how the human mind relates to the world.

A Copernican Revolution
Kant's theory of mind radically revised the way that we all think about
human knowledge of the world. Really. You do not need to have read (or
even heard of ) Kant to be influenced by his ideas, any more than you
need to have read Newton in order to be effected by science.

According to the Rationalist and Empiricist traditions, the mind is
passive either because it finds itself possessing innate, well-formed
ideas ready for analysis, or because it receives ideas of objects into
a kind of empty theater, or blank slate. Kant's crucial insight here is
to argue that experience of a world as we have it is only possible if
the mind provides a systematic structuring of its representations.

So what is this amazing idea of Kant's? In a nutshell, it is the idea
that the structure of the human mind shapes all sensory experience and
thought. The mind has an active
role in producing our conception of reality by acting as a filter, an
organizer, and an enhancer. Kant's ideas is that objective reality is
made possible by the form of its representation. This ideas is called
Kant's Copernican Revolution, because like Nicolaus
Copernicus' (1473-1543) who turned astronomy inside-out by hypothesizing
that the earth moved around the sun (instead of the other way round),
Kant turned epistemology inside-out by theorizing that objective reality
depends on the mind (instead of the other way round).

If I have communicated this idea effectively (and please
understand that this is a barely adequate summary compared to Kant's rigorous
analysis), then you may be saying at this point "So what?"
The idea that the mind filters out parts of the world and participates
in the construction of our understanding is quite ordinary. But that ordinariness
just shows the success for Kant's influence. Before him the battle over
epistemology (theory of knowledge) was between the Rationalists who held
that the mind was composed of innate ideas to which experience conformed
and the Empiricists who held that all ideas, hence the entire mind, came
from experience. On either view, the mind is pictures as a passive receiver
of ideas and perceptions.

Kant showed a way in which the mind can be understood as an active player
in the construction of reality. Not by making things up or inventing ideas,
but by providing the structure into which perception and thought must
conform in order to be representations. This structure includes space,
time, and causation. Before Kant the debate over the concept of space
was whether it was an idea already in the mind at birth and added to perceptions
allowed a mental representation of three-dimensional objects; or whether
space were an idea that formed in the mind as the senses perceived objects
in the three dimensions. After Kant this debate was no longer tenable,
since he had so powerfully shown that space is a precondition of perception.
For instance, there cannot be a perception of color that does not already
have some location in space. The perception of a color may be presented
in many different locations, but there is no perception of color which
has no location at all. Even with your eyes closed, you see the color
patches and specks as having a location in the visual field (which, after
all, has fairly clear spatial boundaries). Thus, we cannot make sense
of the attempt to separate the color-perception from the space-perception.
Space is a condition of (requirement for) color perception, just as time
is a condition of (requirement for) the observation of an event. So space,
time, and causality are conditions of experience (representation of reality).
This is the same as saying that space, time, and causation belong to the
structure of the mind. Note that we are speaking here of the human
mind, not just individual personalities. All humans share some structural
properties. Most animals probably do as well. Perhaps a very alien type
of creature may have a completely different conceptual structure from
that of the human world, but Kant is on firm ground in positing that space,
time, and causation are fundamental conditions for human experience.

Kant draws many remarkable consequences from his central insight. He
seeks to map the structure of the mind, he considers what kinds of knowledge
are possible, he explores what free-will would have to be in such a system,
and very importantly, his analysis of the human conceptual structure leads
to a powerful idea about morality as the freedom to act in accordance
with our own structures of value.